An entirely new type of equation for forecasting atmospheric parameters is derived by applying variational methods to a mathematical model of the atmosphere. The method also defines vertical eigenfunctions to the model. In a simplified case some of the eigenfunctions are compared with empirically obtained data, and conclusions are drawn regarding the validity of some of the approximations in the mathematical model.DOI: 10.1111/j.2153-3490.1977.tb00752.x